Question: $ B = \left[\begin{array}{rr}2 & 2 \\ -1 & 4 \\ 2 & 1\end{array}\right]$ $ E = \left[\begin{array}{rr}1 & 3 \\ 2 & 3 \\ 2 & -2\end{array}\right]$ Is $ B- E$ defined?
Answer: In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ B$ is of dimension $( m \times  n)$ and $ E$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ B$ ) must equal $ p$ (number of rows in $ E$ ) and 2. $ n$ (number of columns in $ B$ ) must equal $ q$ (number of columns in $ E$ Do $ B$ and $ E$ have the same number of rows? Yes Yes No Yes Do $ B$ and $ E$ have the same number of columns? Yes Yes No Yes Since $ B$ has the same dimensions $(3\times2)$ as $ E$ $(3\times2)$, $ B- E$ is defined.